Notating checks is not even redundant; it can disambiguate which piece is to move without additional information (e.g. Rac1 and Rhc1; only one of them might give a discovered check, so Rc1+ could then be an unambiguous notation where the check is not redundant). The PGN spec is clear that SAN disambiguates legal moves and not pieces (if moving one of those rooks would put yourself in check, you should not disambiguate when you move the other one), but I don't know whether it considers the check part of the move for those purposes.
I see what you mean obviously, but neither of those moves could possibly give a discovered check, right? If the rook starts in the corner of the board, nothing can hide behind it or attack from behind it.
> Neither the appearance nor the absence of either a check or checkmating indicator is used for disambiguation purposes. This means that if two (or more) pieces of the same type can move to the same square the differences in checking status of the moves does not allieviate the need for the standard rank and file disabiguation described above. (Note that a difference in checking status for the above may occur only in the case of a discovered check.)